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Can someone please explain the logic behind the explanation given in the official guide for the quantitative review-1st edition (question #117).

In the triangle above, what is the length of the side BC?

(1) Line segment AD has length 6

(2) x= 36

What I can't understand from the explanation is that it has been assumed that

angle ABD + angle DAB = 2x

will imply that ABD = DAB =x.

Why is the above true? Isn't it possible that ABD = 1.5x and DAB = 0.5x?

Why those two have to be equal?

We can no way assume that ABD=DAB=x, from ABD+DAB=2x. If we knew that either ABD or DAB equals to x, then the answer would be A. But in it's current form the answer should be E.

This means that the Official Guide has the wrong answer. Official Guide gives the answer as "A", but I thought ( same as you!) that the answer should be"E".whom shall we inform if the answer in the Official Guide is wrong?